Problem: Solve for $x$ and $y$ using substitution. ${-4x+4y = -12}$ ${y = 2x+2}$
Answer: Since $y$ has already been solved for, substitute $2x+2$ for $y$ in the first equation. ${-4x + 4}{(2x+2)}{= -12}$ Simplify and solve for $x$ $-4x+8x + 8 = -12$ $4x+8 = -12$ $4x+8{-8} = -12{-8}$ $4x = -20$ $\dfrac{4x}{{4}} = \dfrac{-20}{{4}}$ ${x = -5}$ Now that you know ${x = -5}$ , plug it back into $\thinspace {y = 2x+2}\thinspace$ to find $y$ ${y = 2}{(-5)}{ + 2}$ $y = -10 + 2$ $y = -8$ You can also plug ${x = -5}$ into $\thinspace {-4x+4y = -12}\thinspace$ and get the same answer for $y$ : ${-4}{(-5)}{ + 4y = -12}$ ${y = -8}$